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A quantum credo
Physica B 151 (1988) 378-380 North-Holland, A m s t e r d a m
A QUANTUM CREDO Jean-Marc Lt~VY-LEBLOND Physique Thdorique, Universitd de Nice, 28 Parc Valrose, 06034 Nice Cedex, France
Quantum theory now is much more than half a century old. As yet, it has never met with an experimental contradiction, while it has proved able to explain phenomena the orders of magnitude of which range over something like 20 decades in characteristic length and 30 decades in characteristic energy. Among such phenomena, the experiments in neutrons interferometry, in the past years, have beautifully illustrated most intrinsic features of quantum behaviour. My contention then is that we should, at last, take quantum theory seriously; this means accepting and understanding it as it is, before trying to change i t - which no doubt will be necessary some day, but in a direction which we cannot foresee at present. That is to say that I do not believe that we need any "interpretation" of quantum theory. After all, interpreting a text is translating it into another language or explaining it through foreign concepts. That is exactly what usual "interpretations" do, translating back quantum ideas into classical notions most of the time, and trying to explain away its most specific features in terms of ad hoc mechanisms. I hold that quantum theory is consistent as it is, without extraneous assumptions, and that we must deal with it. It is, to my mind, as futile to "interpret" it, as it would be to "interpret" Einsteinian relativity by real Lorentz-Fitzgerald contractions in a Newtonian space-time, or to "interpret" Maxwellian electromagnetism by the vortex motions of the ether, or even to "interpret" the planetary motions by Ptolemaic epicycles-all interpretations which may be consistently adopted. In the same way as we had to accept changing our views about space-time in accordance with Einsteinian relativity, we must change our views about the
nature of physical o b j e c t s - a n d , mainly, accept their essential quantum nonlocality. Furthermore, it seems to me that the real challenge is not so much to "interpret" quantum theory as to understand classical theory . . . . For, if we believe that nucleons, electrons, etc. are ruled by quantum laws, how come that larger pieces of matter, consisting of many such quantums, seem to obey so well classical laws? In other words, I am asking here for an analysis of the status of the classical approximations to quantum theory. That this is not a trivial question is proved by the existence of macroscopic quantum systems (superfluids, supraconductors, laser beams, etc.). To be more specific, here is, in short, my personal quantum credo: 1) Objectivity: There is such a thing as an objective state of a quantum system if (the proviso here is essential) the system is isolated. Such a state may be adequately described by a vector (more precisely, a unit ray) in a certain Hilbert space. The evolution in time of a state vector is always given by a unitary operator. 2) Non-separability: Within a compound system S = (S 1, $2), a subsystem cannot be assigned in general a definite state, but only states relative to those of the complementary subsystem. This is a consequence of 1), of course, since, in general, a state of S does not factorize: 9
4~(1, 2) -- X(1)~b(2),
(1)
but takes the entangled form ~b(1, 2) = ~ Xk(1)ffk(2).
(2)
k
3) Interaction: Interaction between two initial-
0378-4363/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
J.-M. Ldvy-Leblond / A quantum credo
ly isolated subsystems leads them in general from a factorized (separated) state (1) to an entangled state (2). 4) Measurement: A measurement is a special interaction between the measured system and a "measuring apparatus", which has two characteristic features. a) If the system is in a proper state of the measured property, the measuring apparatus is led in a special state, preserving the factorization: gk(1) qJ0(2)---~ Xk(1)~(2) •
lutely equivalent to the clever geocentric TychoBrah6 system. 6) No "many-worlds": The views advocated here are close to those of Everett, but not of its commentators who have introduced the damaging term of "many-worlds interpretation"; neither the word, nor the idea appears in Everett's paper and thesis. In fact, there is one world - but a quantum one. The idea of "many-worlds" or "parallel universes" results from an undue assimilation of a quantum superposition with a classical aggregate; but indeed,
(3) quantum " + " ~ classical " & " .
In general, however, the compound measured system + measuring apparatus goes into an entangled state:
[~-~kC~Xk(1)] qJO(2)-'*~-~kCkXk(1)~Ok(2)"
379
(4)
b) The macroscopic nature of the measuring apparatus results in a vanishing overlap of its own proper states, making the superposition (4) equivalent to an incoherent mixture. It remains, of course, to construct concrete models of quantum measuring apparatus. There are now some examples (Hepp, Cini, etc.), but the task needs generalization and amplification. This last question of course is closely related to the understanding of the classical approximation to quantum theory. 5) No-reduction: Accordingly, there is no "reduction of the wave packet" although everything happens as if there was . . . . The situation here is completely analogous to that of the Copernican system of the world which, from the point of view of specific (Earthbound) observers is abso-
(5)
7) Psychophysiology: These views, the essence of which is to refuse any idea foreign to quantum theory proper (such as the reduction of the wave packet), are completely consistent and sufficient for all practical purposes. The only open question is the one of the subjective human perception, that is, the explanation of why we perceive but a single element in a superposition such as (4). This fact of experience may be described by a suitable interpretation of what is "perception" (Cooper and Van Vechten). But after all, why should we require from quantum physics a complete explanation of complicated psychophysiological phenomena which we do not normally ask from classical physics? Even the perception of sound is far from being completely understood at the psychological level, not to speak of vision (think of the perception of colours; how does the three-receptor theory account for the continuous and complex perception of the coloured spectrum?). Do not ask from quantum theory more than it can give, take first all it may give.
DISCUSSION (Q) Rietdijk: I want to put a question to Prof. L6vy-Leblond. Suppose you open the box of Schr6dinger's cat and find the cat to be dead. Now we m e a s u r e the cat's temperature and find from it that the cat has to be four hours dead. Now the C o p e n h a g e n interpretation states that the cat was both dead and alive before we o p e n e d the box. My question is here: how can the temperature of the cat have suddenly become so
that it corresponds to the cat's being four hours dead if the cat really was dead and alive ("at the same time") before we opened the box? W h a t decides what temperature we find? Did such temperature suddenly originate? I suppose q u a n t u m mechanics does not explain that. (A) J.-M. Ldvy-Leblond: I fully agree with Prof. Green-
380
J.-M. L~vy-Leblond / A quantum credo
berger that this poor cat is not a fair example of a quantum system as it cannot be isolated from the beginning. Its description by a pure quantum state does not make sense. Neither life, nor death are eigenvalues of a dichotomic Hermitian o p e r a t o r . . .
not a black-box-computer. They rely on concepts and express ideas, most of which may look new and strange - but can be simple.
(Q) M. Peshkin: If you had a computer which you may not open, but which merely confirms that this experimental result you fed in is consistent with its program, would that satisfy you? Would you then not seek a theory you could interpret in simple ways?
(Q) J. Clauser (to panelists Greenberger, L6vy-Leblond). What constitutes an apparatus? Certainly not many degrees of freedom: VN problem persists; certainly not isolation - no apparatus can be isolated; certainly not m a c r o s c o p i c macroscopic systems are describable quantum-mechanically. Is there a prescription if I have an object (black box) to say whether or not it is an apparatus?
(A) J.-M. L~vy-Leblond: The whole argument boils down to deciding what is a "simple way". If you believe that a simple explanation is going back to already understood ideas, then of course you will look for classical mechanisms behind the quantum formalism (hidden variables, or the like). I believe that man's mind builds up its notions of simplicity. After all, the heliocentric system was not simple for medieval thinkers. In other words, the equations of quantum theory, for me, are
(A) J.-M. Lgvy-Leblond: It is precisely the goal of a real quantum theory of measurement to tell us what a measuring apparatus is. As I have said above, this is a two-step problem: 1) (easy) defining in a formal way the response properties of the apparatus to coupling with the measured system; 2) (difficult) showing that such properties may indeed be realized by concrete pieces of matter (usually large) ruled, of course, by quantum laws.
A QUANTUM CREDO Jean-Marc Lt~VY-LEBLOND Physique Thdorique, Universitd de Nice, 28 Parc Valrose, 06034 Nice Cedex, France
Quantum theory now is much more than half a century old. As yet, it has never met with an experimental contradiction, while it has proved able to explain phenomena the orders of magnitude of which range over something like 20 decades in characteristic length and 30 decades in characteristic energy. Among such phenomena, the experiments in neutrons interferometry, in the past years, have beautifully illustrated most intrinsic features of quantum behaviour. My contention then is that we should, at last, take quantum theory seriously; this means accepting and understanding it as it is, before trying to change i t - which no doubt will be necessary some day, but in a direction which we cannot foresee at present. That is to say that I do not believe that we need any "interpretation" of quantum theory. After all, interpreting a text is translating it into another language or explaining it through foreign concepts. That is exactly what usual "interpretations" do, translating back quantum ideas into classical notions most of the time, and trying to explain away its most specific features in terms of ad hoc mechanisms. I hold that quantum theory is consistent as it is, without extraneous assumptions, and that we must deal with it. It is, to my mind, as futile to "interpret" it, as it would be to "interpret" Einsteinian relativity by real Lorentz-Fitzgerald contractions in a Newtonian space-time, or to "interpret" Maxwellian electromagnetism by the vortex motions of the ether, or even to "interpret" the planetary motions by Ptolemaic epicycles-all interpretations which may be consistently adopted. In the same way as we had to accept changing our views about space-time in accordance with Einsteinian relativity, we must change our views about the
nature of physical o b j e c t s - a n d , mainly, accept their essential quantum nonlocality. Furthermore, it seems to me that the real challenge is not so much to "interpret" quantum theory as to understand classical theory . . . . For, if we believe that nucleons, electrons, etc. are ruled by quantum laws, how come that larger pieces of matter, consisting of many such quantums, seem to obey so well classical laws? In other words, I am asking here for an analysis of the status of the classical approximations to quantum theory. That this is not a trivial question is proved by the existence of macroscopic quantum systems (superfluids, supraconductors, laser beams, etc.). To be more specific, here is, in short, my personal quantum credo: 1) Objectivity: There is such a thing as an objective state of a quantum system if (the proviso here is essential) the system is isolated. Such a state may be adequately described by a vector (more precisely, a unit ray) in a certain Hilbert space. The evolution in time of a state vector is always given by a unitary operator. 2) Non-separability: Within a compound system S = (S 1, $2), a subsystem cannot be assigned in general a definite state, but only states relative to those of the complementary subsystem. This is a consequence of 1), of course, since, in general, a state of S does not factorize: 9
4~(1, 2) -- X(1)~b(2),
(1)
but takes the entangled form ~b(1, 2) = ~ Xk(1)ffk(2).
(2)
k
3) Interaction: Interaction between two initial-
0378-4363/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
J.-M. Ldvy-Leblond / A quantum credo
ly isolated subsystems leads them in general from a factorized (separated) state (1) to an entangled state (2). 4) Measurement: A measurement is a special interaction between the measured system and a "measuring apparatus", which has two characteristic features. a) If the system is in a proper state of the measured property, the measuring apparatus is led in a special state, preserving the factorization: gk(1) qJ0(2)---~ Xk(1)~(2) •
lutely equivalent to the clever geocentric TychoBrah6 system. 6) No "many-worlds": The views advocated here are close to those of Everett, but not of its commentators who have introduced the damaging term of "many-worlds interpretation"; neither the word, nor the idea appears in Everett's paper and thesis. In fact, there is one world - but a quantum one. The idea of "many-worlds" or "parallel universes" results from an undue assimilation of a quantum superposition with a classical aggregate; but indeed,
(3) quantum " + " ~ classical " & " .
In general, however, the compound measured system + measuring apparatus goes into an entangled state:
[~-~kC~Xk(1)] qJO(2)-'*~-~kCkXk(1)~Ok(2)"
379
(4)
b) The macroscopic nature of the measuring apparatus results in a vanishing overlap of its own proper states, making the superposition (4) equivalent to an incoherent mixture. It remains, of course, to construct concrete models of quantum measuring apparatus. There are now some examples (Hepp, Cini, etc.), but the task needs generalization and amplification. This last question of course is closely related to the understanding of the classical approximation to quantum theory. 5) No-reduction: Accordingly, there is no "reduction of the wave packet" although everything happens as if there was . . . . The situation here is completely analogous to that of the Copernican system of the world which, from the point of view of specific (Earthbound) observers is abso-
(5)
7) Psychophysiology: These views, the essence of which is to refuse any idea foreign to quantum theory proper (such as the reduction of the wave packet), are completely consistent and sufficient for all practical purposes. The only open question is the one of the subjective human perception, that is, the explanation of why we perceive but a single element in a superposition such as (4). This fact of experience may be described by a suitable interpretation of what is "perception" (Cooper and Van Vechten). But after all, why should we require from quantum physics a complete explanation of complicated psychophysiological phenomena which we do not normally ask from classical physics? Even the perception of sound is far from being completely understood at the psychological level, not to speak of vision (think of the perception of colours; how does the three-receptor theory account for the continuous and complex perception of the coloured spectrum?). Do not ask from quantum theory more than it can give, take first all it may give.
DISCUSSION (Q) Rietdijk: I want to put a question to Prof. L6vy-Leblond. Suppose you open the box of Schr6dinger's cat and find the cat to be dead. Now we m e a s u r e the cat's temperature and find from it that the cat has to be four hours dead. Now the C o p e n h a g e n interpretation states that the cat was both dead and alive before we o p e n e d the box. My question is here: how can the temperature of the cat have suddenly become so
that it corresponds to the cat's being four hours dead if the cat really was dead and alive ("at the same time") before we opened the box? W h a t decides what temperature we find? Did such temperature suddenly originate? I suppose q u a n t u m mechanics does not explain that. (A) J.-M. Ldvy-Leblond: I fully agree with Prof. Green-
380
J.-M. L~vy-Leblond / A quantum credo
berger that this poor cat is not a fair example of a quantum system as it cannot be isolated from the beginning. Its description by a pure quantum state does not make sense. Neither life, nor death are eigenvalues of a dichotomic Hermitian o p e r a t o r . . .
not a black-box-computer. They rely on concepts and express ideas, most of which may look new and strange - but can be simple.
(Q) M. Peshkin: If you had a computer which you may not open, but which merely confirms that this experimental result you fed in is consistent with its program, would that satisfy you? Would you then not seek a theory you could interpret in simple ways?
(Q) J. Clauser (to panelists Greenberger, L6vy-Leblond). What constitutes an apparatus? Certainly not many degrees of freedom: VN problem persists; certainly not isolation - no apparatus can be isolated; certainly not m a c r o s c o p i c macroscopic systems are describable quantum-mechanically. Is there a prescription if I have an object (black box) to say whether or not it is an apparatus?
(A) J.-M. L~vy-Leblond: The whole argument boils down to deciding what is a "simple way". If you believe that a simple explanation is going back to already understood ideas, then of course you will look for classical mechanisms behind the quantum formalism (hidden variables, or the like). I believe that man's mind builds up its notions of simplicity. After all, the heliocentric system was not simple for medieval thinkers. In other words, the equations of quantum theory, for me, are
(A) J.-M. Lgvy-Leblond: It is precisely the goal of a real quantum theory of measurement to tell us what a measuring apparatus is. As I have said above, this is a two-step problem: 1) (easy) defining in a formal way the response properties of the apparatus to coupling with the measured system; 2) (difficult) showing that such properties may indeed be realized by concrete pieces of matter (usually large) ruled, of course, by quantum laws.